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Q. No.Two blocks \(A, B\) of mass \(1\) kg, \(2\) kg are connected by means of a light spring of spring constant \(k=10\) N/m. The system is placed at rest on a smooth horizontal plane, and a horizontal force \(F=2\) N is applied to the block \(B,\) as shown.
The acceleration of the centre of mass of the system is:
1.
\(\dfrac23\) m/s2 initially, but it varies with time.
2.
\(\dfrac23\) m/s2 and is constant.
3.
zero initially, but it reaches a maximum of \(1\) m/s2.
4.
\(1\) m/s2 initially, but it decreases thereafter with time.
Subtopic: Center of Mass |
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Two point masses, \(m_{A}=2\) g and \(m_{B}=3\) g, are connected by a massless rod of length \(1\) m (see figure). The centre-of-mass of the system will lie at a distance of:
1. \(0.4\) m from \(m_{A}\)
2. \(0.6\) m from \(m_{A}\)
3. \(0.5\) m from \(m_{A}\)
4. \(0.7\) m from \(m_{A}\)
1. \(0.4\) m from \(m_{A}\)
2. \(0.6\) m from \(m_{A}\)
3. \(0.5\) m from \(m_{A}\)
4. \(0.7\) m from \(m_{A}\)
Subtopic: Center of Mass |
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A \(\sqrt {34}\) m long ladder weighing \(10\) kg leans on a frictionless wall. Its feet rest on the floor \(3\) m away from the wall as shown in the figure. If \(\mathrm F_ \mathrm f\) and \(\mathrm F_ \mathrm w\) are the reaction forces of the floor and the wall, then ratio of \(\mathrm F_ \mathrm w / \mathrm F_ \mathrm f\) will be: (Take \(g=10\) m/s2)
1. \(\dfrac{6}{\sqrt{110}} \)
2. \(\dfrac{3}{\sqrt{113}} \)
3. \(\dfrac{3}{\sqrt{109}} \)
4. \( \dfrac{2}{\sqrt{109}}\)
1. \(\dfrac{6}{\sqrt{110}} \)
2. \(\dfrac{3}{\sqrt{113}} \)
3. \(\dfrac{3}{\sqrt{109}} \)
4. \( \dfrac{2}{\sqrt{109}}\)
Subtopic: Torque |
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A man standing on a still boat jumps out horizontally with a speed of \(20~\text{m/s}\) with respect to the boat. If the mass of the man is \(70~\text{kg}\) and that of the boat is \(210~\text{kg},\) then the speed of the boat after the man jumps will be:
1. \(20~\text{m/s}\)
2. \(6.67~\text{m/s}\)
3. \(5~\text{m/s}\)
4. \(15~\text{m/s}\)
1. \(20~\text{m/s}\)
2. \(6.67~\text{m/s}\)
3. \(5~\text{m/s}\)
4. \(15~\text{m/s}\)
Subtopic: Linear Momentum |
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A man and a plank system are moving horizontally on a smooth surface with a velocity of \(10~\text{m/s}.\) With what velocity should the man jump out of the plank so that the plank comes to rest if the mass of the plank is double the mass of the man?
1. \(10~\text{m/s}\)
2. \(20~\text{m/s}\)
3. \(30~\text{m/s}\)
4. not possible
1. \(10~\text{m/s}\)
2. \(20~\text{m/s}\)
3. \(30~\text{m/s}\)
4. not possible
Subtopic: Linear Momentum |
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For the alphabet \(V\) made from a thin uniform wire as shown, the centre-of-mass will be at:
1. \((0,0)\)
2. \((0,3)\)
3. \((3,0)\)
4. \((2,3)\)
1. \((0,0)\)
2. \((0,3)\)
3. \((3,0)\)
4. \((2,3)\)
Subtopic: Center of Mass |
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A pulley of radius \(1.5~\text m\) is rotated about its axis by a force, \(F=(12t-3t^{2})~\text N\) applied tangentially (while \(t\) is measured in seconds). If the moment of inertia of the pulley about its axis of rotation is \(4.5~\text{kg-m}^2,\) the number of rotations made by the pulley before its direction of motion is reversed, will be \(\dfrac K \pi\). The value of \(K\) is:
| 1. | \(12\) | 2. | \(14\) |
| 3. | \(16\) | 4. | \(18\) |
Subtopic: Rotational Motion: Dynamics |
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Level 3: 35%-60%
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The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are:
| 1. | \(1 : \sqrt 2\) | 2. | \(3:2\) |
| 3. | \(2:1\) | 4. | \( \sqrt 2 : 1 \) |
Subtopic: Moment of Inertia |
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Two discs are rotating about their respective axes, which are normal to the discs and pass through their centres. Disc \(D_1\) has a \(2\) kg mass and \(0.2\) m radius and an initial angular velocity of \(50~\text{rad} ~\text{s}^{-1}.\) Disc \(D_2\) has a \(4\) kg mass, \(0.1\) m radius and an initial angular velocity of \(200~\text{rad} ~\text{s}^{-1}.\) The two discs are brought into contact face to face, with their axes of rotation coincident. The final angular velocity (in \(\text{rad} ~\text{s}^{-1}\)) of the combined system is:
1. \(60\)
2. \(100\)
3. \(120\)
4. \(40\)
1. \(60\)
2. \(100\)
3. \(120\)
4. \(40\)
Subtopic: Angular Momentum |
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Level 2: 60%+
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A force is applied to a hollow spherical shell so that it acts through its centre. It causes an acceleration of \(3\) m/s2. If the same force is applied to the spherical shell, acting tangent to its surface, the acceleration will be: (Assuming no friction is available.)
| 1. | \(3\) m/s2 | 2. | \(2\) m/s2 |
| 3. | zero | 4. | \(1\) m/s2 |
Subtopic: Rotational Motion: Dynamics |
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Level 3: 35%-60%
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